PORTFOLIO MANAGEMENT

Portfolio: Portfolio is the combination of more than one security. That is combination shares,

debentures, etc..

Portfolio Construction Approaches:There are two approaches;

1. Traditional Approach.2. Modern Approach. (Markowitz efficient frontier Model)

Traditional Approach Individual specific planning Individual in nature. Individual consideration.

Steps for Portfolio construction is Traditional approach:1. Analyzing the constraints 2. Determination of objectives.3. Selection of portfolio.4. Risk return analysis5. Diversification.

Modern Approach: Portfolio theory, originally proposed by Harry Markowitz in the 1950s, was the first formal attempt to quantify the risk of a portfolio and develop a methodology for determining the optimal portfolio. Prior to the development of portfolio theory, investors dealt with the concepts of return & risk somewhat loosely. Intuitively smart investors knew the benefit of diversification which is reflected in the traditional approach “Do not put all your eggs in one basket.” Harry Markowitz was the first person to show quantitatively why and how diversification reduces risk.

TYPES OF RISK

SYSTEMATIC RISK & UNSYSTEMATIC RISK Risk consists of two components, the systematic risk and unsystematic risk. The

systematic risk is caused by factors external to the particular company and uncontrollable by the company. The systematic risk affects the markets as a whole. In case of unsystematic risk the factors are specific unique and related to the particular industry or company.

Systematic Risk: The systematic risk affects the entire market. Often we read in the news papers that the stock market is in the bear bug or in the bull grip. This indicates that the entire market is moving in a particular direction either downward or upward. The economic conditions, political situations and the sociological changes affect the security market. These factors are beyond the

control of the corporate and the investor. They cannot be entirely avoided by the investor. It drives home the point that the systematic risk is unavoidable.

The systematic risk is further sub-divided into:1. Market Risk2. Interest Rate Risk3. Purchasing Power Risk.

MARKET RISK: Jack Clark Francis defined market risk as that portion of total variability of return caused by the alternating forces of bull and bear markets. When the security index moves upward haltingly for a significant period of time, it is known as bull market. In the bull market, the index moves form low level to the peak. Bear market is just reverse to a market low point for a significant period to time.

The forces that affect the stock market are tangible and intangible events. The tangible events are real events such as earthquake, political uncertainty, fall in the value of currently etc. Intangible events are related to market psychology.

Interest Rate Risk: Interest rate risk is the variation in the single period rates of return caused by the fluctuations in the interest rate. Most commonly interest rate risk affects the price of bonds, debentures and stocks. The fluctuations in the interest rates are caused by the changes in the government monetary policy and the changes that occur in the interest rates of treasury bills and the governments bonds. The bonds issued by government and quasi government are considered to be risk free. If higher interest rates are offered, investor would like to switch his investment form private sector bonds to public sector bonds.

Like wise, if stock market is in a depressed condition, investors would like to shift their money to the bond market, to have an assured rate of return.

The rise of fall in the interest rates affects the cost of borrowings. Most of the stock traders trade in the stock market with the borrowed funds. The increase in the cost of margin affects the profitability of the traders.

Interest rates also affect the corporate bodies that carry their business with borrowed funds.

Purchasing Power Risk: Variations in the returns are caused also by the lose of purchasing power of currency. Inflation is the reason behind the loss of purchasing power. The level of inflation proceeds faster than the increase in capital value. Purchasing power risk is the probable loss in the purchasing power of the returns to be received. The rise in the price penalizes the returns to the investor and every potential rise in price is a risk to the investor.

UNSYSTEMATIC RISK: As already discussed, unsystematic risk is unique and peculiar to a firm or an industry. Unsystematic risk stems form managerial inefficiency, technological change in the production process, change in the customer preferences, labour problems etc. Unsystematic risk can be classified into;1. Business Risk2. Financial Risk.

Business Risk: it is that portion of the unsystematic risk caused by the operating environment of the business. Business risk arise form the inability of a firm to maintain its competitive edge and

the growth or stability of the earnings. Variation that occurs in the operating income expected operating income indicates the business risk.

Business risk can be divided into external business risk and internal business risk.

Internal Business Risk: Internal Business risk is associated with the operational efficiency of the firm. The operational efficiency differ form company to company.

Fluctuations in the sales Research & Development Personnel Management Fixed cost Single Product.

External Risk: External risk is the result of operating conditions imposed on the firm by circumstance beyond its control. The external factors are social, monetary & fiscal policies of the government, business cycles general economic environment etc.

These factors are mainly divided into:1. Social & Regulatory factors2. Political Risk3. Business Cycle.

Financial Risk: It refers to the variability of the income to the equity capital due to the debt capital. Financial risk in the company is associated with the capital structure of the company.

THE CHARACTERISTIC REGRESSION LINE (CRL)The characteristic regression line is a simple linear regression model estimated for a

particular stock against the market index return to measure its diversifiable and undiversifiable risks. The model is,

Ri = αi + βiRm + ei

Ri = Return of the ith stock. αi = Interceptβi = Slope of ith stockRm = Return of the market indexei = The error term.

The security return is – Today’s price - Yesterday’s priceToday’s Security return = -------------------------------------------- × 100 Yesterday’s price

Today’s Index – Yesterday’s IndexToday’s Market return = ---------------------------------------------× 100 Yesterday’s index

To calculate beta, the returns have to be calculated then using the formula the beta and alpha co-efficient can be calculated.

β = 1

α

β > 1

α

Stock

return

Market ReturnMarket Return

Stock

return

β <1

α

Stock

return

Market Return

A B C

nΣ XY – (ΣX) (ΣY) β= --------------------------- nΣ X2 – (Σ X) 2 _ _α = Y – βX

Calculation of Residual variance:

ΣY2 - α ΣY - β ΣXe2 = --------------------------- n e2= e2

Beta: Beta is the slope of the characteristic regression line. Beta describes the relationship between the stock’s return and the index return.

Beta = +1.0: One % change in market index return causes exactly one % change in stock return.

Beta = +0.5: One % change in market index return causes 0.5 % change in stock return. The stock is less volatile compared to the market.

Beta = +2.0: One % change in market index return causes 2 % change in stock return. The stock return is more volatile.

Negative Beta Value: It indicates that the stock return moves in the opposite direction to the market return.

A- Systematic Risk as Market.B- High Systematic Risk.C- Low Systematic Risk.

Alpha: The intercept of the characteristic regression line is alpha. It is the difference between the horizontal axis and line’s intersection with y-axis. It measures unsystematic risk of the company. It indicates that stock return is independent of the market return. A positive alpha is a healthy sign.

Beta: Beta measures the systematic risk which cannot be eliminated.

THE EXPECTED RETURN ON PORTFOLIO OF RISKKY ASSETSThe portfolio analysis we often want to know the expected (or anticipated) return on a

portfolio of risky assets.The expected return on a portfolio is:

Where E(Rp) = Expected return on a portfolio. Wi = Weight of asset i in the portfolio E(Ri) = Expected return on asset;

E(Rp) = ΣWi E(R1)

PORTFOLIO RISK : Holding two securities may reduce the portfolio risk too. The portfolio risk can be calculated with the help of following formula;

σp = Portfolio standard deviation W1 = Weight of the asset (1) in portfolioW2 = Weight of the asset (2) in portfolio σ1 = SD of Stock1

σ2 = SD of Stock2 r12 = Correlation in co-efficient of W1 & W2

σA2 = ∑Pi [ RA,I – E(RA) ]2

σB2 = ∑Pi [ RB,I – E(RB) ]2

σA,B = ∑Pi [ RA,I – E(RA) ] [ RB,I – E(RB) ]

σA2, σB

2 = Variance of returns on investments A & B.

Pi = Probability of the state of nature;

E(Rp) = Wi E(R1) + W2 E(R2) + ...................+ Wn E(Rn)

σp = Wi2σi

2 + W22σ2

2 + 2W1W2 (r12σ1σ2)

σA,B rA,B = ------------ σA×σB

σA,B βA,B = ----------- σB

2

RA, RB = Holding period return on investments A & B if the state of nature i occurs.E(RA), E(RB) = Expected return on investments A & B.σA,B = Co – variance of the returns on investments A & B.rA,B = Co – efficient of correlation of the returns on investments A & BσA, σB = Standard deviations of returns.βA,B = Beta of return on A with respect to B.

CAPM & APT

Capital Asset Pricing ModelHarry Markowitz developed an approach that helps an investor to achieve his optimal

portfolio position. Hence, portfolio theory, in essence, has a normative character as it prescribes what a rational investor should do.

William Sharpe and others asked the follow-up question: If rational investors follow the Markowitzian prescription, what kind of relationship exists between risk and return? Essentially, the capital asset pricing model (CAPM) developed by them is an exercise in positive economics. It is concerned with two key questions:

What is the relationship between risk and return for an efficient portfolio? What is the relationship between risk and return for an individual security?The CAPM, is essence, predicts the relationship between the risk of an asset and its expected

return. This relationship is very useful in two important ways. First, it produces a benchmark for evaluating various investments. Second, it helps us to make an informed guess about the return that can be expected from an asset that has not yet been traded in the market.

Although the empirical evidence on the CAPM is mixed, it is widely used because of the valuable insight it offers and its accuracy is deemed satisfactory for most practical applications.

CAPM is discussed as fallows:-1. Basic assumptions2. Capital Market Line (CML)3. Security Market Line (SML)4. Inputs required for CAPM5. Empirical evidence on CAPM.

BASIC ASSUMPTIONS

The CAPM is based on the following assumptions:1. Individuals are risk averse.2. Individuals seek to maximize the expected utility of their portfolio over a single period

planning horizon.3. Individuals have homogeneous expectations – they have identical subjective estimates of

the means, variances and covariance among returns4. Individuals can borrow and lend freely at a riskless rate of interest.5. The market is perfect; there are no taxes; there are no transaction costs; securities are

completely divisible; market is competitive.6. The quantity of risky securities in the market is given.

Risk is measured by variance of expected returns there are two components of risk systematic (non – diversifiable) and unsystematic (diversifiable). For diversifiable risk, the investor makes proper diversification to reduce the risk. For the non – diversifiable portion, he uses the relevant Beta measure to adjst to his requirements. Due to the possibility of risk free asset and lending and borrowing at risk free interest rates, the investors have two components of the portfolio – risk free assets and risky assets.The expected return on the combination of risky and risk free combination is;Rp = RfXf + Rm (1 – Xf )

Rp = Return on portfolioXf = Proportion of funds invested in the risk free assets.

Rf = Risk free rate of returnRm= Return on risky assets.1-Xf = Proportion of funds invested in the risky assets.

CAPITAL MARKET LINE (CML)

y Z CML Rp CML

Rm M B C Rm – Rf (Measure of Risk premium

Rf A

(Risk less return)

Fig – 1 Fig – 2

Figure – 1

Point ‘Rf’ is the risk less interest rate. Preferred investments are plotted along the line R f MZ, by the combination of both risky assets and risk free assets, along with borrowing and lending. This is known as CML. It gives desirable set of investment opportunities between risk free and risky investments. The slope of Rf MZ is the measure of the reward for risk taking. P is the risk free return. Rm – Rf is the measure of the risk premium – a return for the risk taking.

Figure – 2

The line Rf B represents all possible combination of risk less and risky assets. The portfolio along with the path Rf B is called lending portfolio. If it crosses B it becomes borrowing portfolio. (Combination of risky portfolio with borrowing). Borrowing increases both the expected return and the risk while lending (i,e combining risky portfolio with risk free asset) reduces the expected return & risk.Thus the investors with high risk aversion will prefer to lend and thus hold a combination of risky asset and risk free asset. Others with less risk aversion will borrow and invest more in the risky portfolio, ABC represent efficient frontier. ABC line show the investor’s portfolio of risky assets. The investors can combine risk less asset either by lending or borrowing.

ABC is concave curve represent an efficient frontier of risky portfolios.Introduction of borrowing and lending gives us an efficient frontier that is straight line

through out. E (Rm – Rf) E(Rp) = Rf +-------------------× σp

σm

E(Rp) = Portfolio’s expected return.

Expected Return

Risk (σ)

Risk (σ)

Rm = Expected return on the market portfolio.σm = Standard deviation of market portfolio.σp = Standard deviation of the portfolio.

SECURITY MARKET LINEThe risk-return relationship of an efficient portfolio is measured by the capital market

line. All portfolios other than efficient portfolios will lie below the CML. The CML does not describe the risk – return relationship of inefficient portfolios of individual securities. The CAPM specifies the relationship between expected return and risk for all securities and all portfolios, whether efficient of inefficient.

We have seen earlier that the total risk of a security as measured by standard deviation is composed of two components; systematic risk & unsystematic risk of diversifiable risk. As Investment is diversified and more and more securities are added to a portfolio, unsystematic risk tends to become zero and the only relevant risk is systematic risk measured by Beta (β). Hence it is argued that, the correct measure of security risk is beta. The beta analysis is useful for individual securities and portfolios whether efficient of inefficient.

The relationship between expected return and β of a security can be determined graphically. Lit us consider an XY graph where the expected returns are plotted on the OY axis and beta coefficient on OX axis. A risk free asset has expected return equivalent to R f and beta co – efficient is zero (0). The Market Portfolio M has a beta co – efficient of I and expected return equivalent to Rm. A straight line joining these tow point is known as the Security Market Line (SML). The SML helps to determine the expected return for a given security beta. This is explained in the following figure.

The Security Market Line provides the relationship between the expected return and beta of a security or portfolio. This relationship can be expressed in the form of the following equation.E(Rj) = Rf + βi [ E(Rm) – Rf ]Inputs required for applying CAPM Risk free rate Market risk premium Beta.

SMLM

Rf

Rm

Rp

BetaI

Security Market Line

CAPM & Capital Budgeting:We can apply the CAPM to figure out a projects required rate of return.

Equity Beta and Asset Beta: βE

βE = βA [ 1 + D/E ( 1 – T) ] βA = ------------------------

[ 1 + D/E(1 – T )

Procedure for calculation a project’s required rate of return; (as per CAPM)

Find a sample of firms engaged in the same line of business. Obtain equity betas for the sample firms Derive assets betas Find the average of the asset betas Figure out the equity beta for the proposed project. Estimate cost equity re = Rf (Rm – Rf) β Calculate the project’s required rate of return

rA = WE rE + WDrD (1 – T)

rA = Weighted average cost of capital.

Pricing of securities with CAPM:

Evaluation of securities:

T S x R x C x B x A x x x x W x V U

0.7 1.0 1.3

Estimated return

Rf

Beta